The paper introduces the expected sample complexity metric for stochastic multi‑armed bandits and analyzes it within a new framework called approximately correct in expectation (ACE). It demonstrates that ACE guarantees lead to almost sure convergence to the optimal expected reward, contrasts this with high‑probability guarantees, and shows how to translate ACE bounds into explicit expected regret bounds. The authors prove that deterministic algorithms cannot achieve favorable ACE bounds, propose an explore‑then‑ε‑greedy algorithm when ε is known, analyze Thompson sampling when ε is unknown, and provide nearly matching lower bounds that establish tightness and a performance separation between the two regimes.
By Nadav Sukenik, Nadav Merlis
arXiv:2402. 07391v3 Announce Type: replace-cross Abstract: We consider a replicable stochastic multi-armed bandit algorithm that ensures, with high probability, that the algorithm's sequence of actions is not affected by the randomness inherent in the dataset.
By Junpei Komiyama, Shinji Ito, Yuichi Yoshida, Souta Koshino
The paper presents the first high‑probability regret bounds for both cumulative and current‑step variants of Feel‑Good Thompson Sampling (FGTS) in contextual bandits with general realizable function approximation. The bounds rely on decoupling coefficients and prior mass near the true reward function, and in the linear setting they achieve ≠d√T log(2T)+√T log(1/δ) regret with probability at least 1‑δ. This matches the dimension and horizon dependence of upper‑confidence‑bound algorithms up to logarithmic factors, while the high‑probability cost adds only linear dependence on log(1/δ).
By Xuheng Li, Qingyue Zhao, Quanquan Gu
arXiv:2409. 18909v2 Announce Type: replace Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret.
By Junwen Yang, Vincent Y. F. Tan, Tianyuan Jin
arXiv:2606. 04931v1 Announce Type: new Abstract: Mean-based algorithms are a class of online learning algorithms that assign low probability to actions with low average rewards.
By Julius Durmann, Amelie Kleber
arXiv:2610.01951v1 Announce Type: cross
Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well u...
By Nam Nguyen, Tuan Quang Dam
arXiv:2602. 08026v2 Announce Type: replace Abstract: We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits.
By David Janz, Arya Akhavan, Csaba Szepesv\'ari
arXiv:2502. 13467v2 Announce Type: replace Abstract: The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms.
By Yu Chen, Siwei Wang, Longbo Huang, Wei Chen
arXiv:2605. 09454v2 Announce Type: replace-cross Abstract: We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function.
By Devdan Dey, Sujoy Bhore, Avishek Ghosh
arXiv:2606. 28616v1 Announce Type: new Abstract: In stochastic linear bandits, the canonical Upper Confidence Bound (UCB) algorithm admits a simple frequentist regret analysis but can be computationally demanding, while Thompson Sampling (TS) is computationally attractive yet typically harder to analyze due to its non-optimistic nature.
By Toshinori Kitamura, Shuai Liu, Csaba Szepesv\'ari
arXiv:2606. 01799v1 Announce Type: new Abstract: We study $N$-armed stochastic dueling bandits under the Condorcet-winner assumption, where three widely adopted objectives are considered: best-arm identification (BAI), weak regret, and strong regret.
By Pu Wang, Yao-Xiang Ding
arXiv:2608.01069v2 Announce Type: replace
Abstract: Bandit algorithms generate data for downstream inference, but adaptive sampling biases post-bandit sample means. We analyze this bias for stable in...
By Lisu Wang, Yilun Chen, Jiaqi Lu